Problem: Problem

Given a sequence $ A $ of length $ H $ and a sequence $ B $ of length $ W $.

Define the matrix $ C $ consisting of $ H $ rows and $ W $ columns as follows.
$ C_ {i, j} = A_i \ times B_j (1 \ leq i \ leq H, 1 \ leq j \ leq W) $

Process the following four types of queries a total of $ Q $ times.

Query 1
$ 1 $ $ a $ $ b $ $ v $
$ A_i (a \ leq i \ leq b) Add $ v $ to $

Query 2
$ 2 $ $ c $ $ d $ $ v $
$ B_j (c \ leq j \ leq d) Add $ v $ to $

Query 3
$ 3 $ $ a $ $ b $ $ c $ $ d $
$ C_ {i, j} (a \ leq i \ leq b, c \ leq j \ leq d) Output the minimum value of $ and its number

Query 4
$ 4 $ $ a $ $ b $ $ c $ $ d $
$ C_ {i, j} (a \ leq i \ leq b, c \ leq j \ leq d) Output the maximum value of $ and its number

For details, refer to sample input / output.

Constraints

The input satisfies the following conditions.

* $ 1 \ leq H, W, Q \ leq 10 ^ 5 $
* $ -1000 \ leq A_i \ leq 1000 $
* $ -1000 \ leq B_j \ leq 1000 $



For each query, the input satisfies the following conditions.


* $ 1 \ leq a \ leq b \ leq H $
* $ 1 \ leq c \ leq d \ leq W $
* $ -1000 \ leq v \ leq 1000 $

Input

The input is given in the following format.


$ H $ $ W $ $ Q $
$ A_1 $ $ A_2 $ ... $ A_H $
$ B_1 $ $ B_2 $ ... $ B_W $
$ query_1 $
$ query_2 $
...
$ query_Q $


Each query is given in one of the following four formats.


$ 1 $ $ a $ $ b $ $ v $
$ 2 $ $ c $ $ d $ $ v $
$ 3 $ $ a $ $ b $ $ c $ $ d $
$ 4 $ $ a $ $ b $ $ c $ $ d $


All inputs are given as integers.
$ H $, $ W $, $ Q $ are given on the first line, separated by blanks.
In the second row, the element $ A_i $ ($ 1 \ leq i \ leq H $) of the sequence $ A $ is given, separated by blanks.
In the third row, the element $ B_j $ ($ 1 \ leq j \ leq W $) of the sequence $ B $ is given, separated by blanks.
Queries are given on the 4th and subsequent $ Q $ lines, separated by line breaks.
All numbers in each query are separated by blanks.

Output

For each query 3 and query 4, output the value and number on one line, separated by blanks.

Examples

Input

4 4 7
1 2 3 4
1 2 3 4
3 2 3 2 3
4 2 3 2 3
3 1 1 1 1
4 1 1 1 1
1 1 1 1
3 1 4 1 2
4 2 3 2 4


Output

4 1
9 1
1 1
1 1
2 2
12 1


Input

4 4 6
1 1 1 1
1 1 1 1
3 1 4 1 4
4 1 4 1 4
1 2 3 1
2 2 3 1
3 1 4 1 4
4 1 4 1 4


Output

1 16
1 16
1 4
4 4


Input

4 4 7
0 1 0 1
1 0 1 0
3 2 4 1 3
4 1 4 1 4
1 1 4 -1
3 1 3 1 3
1 3 3 2
2 3 3 -2
3 2 4 2 4


Output

0 5
1 4
-1 4
-1 1


Input

36 4 20
-523 -460 -536 -885 652 782 513 -558 -521 -808 124 -708 -943 52 -856 -755 -958 913 380 -767 373 -731 -492 213 538 392 -39 509 -840 135 78 -285 -241 522 -572 -915
-691 -16 812 -385
4 7 17 4 4
3 24 33 1 1
4 3 35 2 4
3 28 32 4 4
2 3 3 438
3 7 15 1 1
4 2 17 4 4
3 24 28 2 4
4 15 16 4 4
4 18 29 1 1
3 24 27 2 4
2 2 3 -828
3 18 23 3 3
1 27 31 -701
2 2 3 298
1 21 32 237
2 3 3 -71
1 14 29 772
4 13 19 3 3
3 19 34 1 2


Output

368830 1
-371758 1
741356 1
-195965 1
-354483 1
368830 1
-207130 1
329560 1
580440 1
-207130 1
-323674 1
1093565 1
-1068977 1

Solution (in CPP):

Solution:
 #include <bits/stdc++.h>
                                        #include<iostream>
                                        #include<cstdio>
                                        #include<vector>
                                        #include<queue>
                                        #include<map>
                                        #include<cstring>
                                        #include<string>
                                        #include <math.h>
                                        #include<algorithm>
                                    //    #include <boost/multiprecision/cpp_int.hpp>
                                        #include<functional>
                               #define int long long
                                        #define inf  1000000007
                                        #define pa pair<int,int>
                                        #define ll long long
                                        #define pal pair<double,double>
                                        #define ppap pair<pa,int>
                                  
                                        #define ssa pair<string,int>
                                        #define  mp make_pair
                                        #define  pb push_back
                                        #define EPS (1e-10)
                                        #define equals(a,b) (fabs((a)-(b))<EPS)
int dx[4]={0,-1,0,1};
int dy[4]={1,0,-1,0};
                                        using namespace std;
                               			class pa3{
                                        	public:
                                        	int x,y,z;
                                        	pa3(int x=0,int y=0,int z=0):x(x),y(y),z(z) {}
                                        	bool operator < (const pa3 &p) const{
                                        		if(x!=p.x) return x<p.x;
                                        		if(y!=p.y) return y<p.y;
                                        		 return z<p.z;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                               				bool operator > (const pa3 &p) const{
                                        		if(x!=p.x) return x>p.x;
                                        		if(y!=p.y) return y>p.y;
                                        		 return z>p.z;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa3 &p) const{
                                        		return x==p.x && y==p.y && z==p.z;
                                        	}
                                        		bool operator != (const pa3 &p) const{
                                        			return !( x==p.x && y==p.y && z==p.z);
                                        	}
                                        
                                        };
                                        
                                        class pa4{
                                        	public:
                                        	double x;
                                        	int y,z,w;
                                        	pa4(double x=0,int y=0,int z=0,int w=0):x(x),y(y),z(z),w(w) {}
                                        	bool operator < (const pa4 &p) const{
                                        		if(x!=p.x) return x<p.x;
                                        		if(y!=p.y) return y<p.y;
                                        		if(z!=p.z)return z<p.z;
                                        		return w<p.w;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator > (const pa4 &p) const{
                                        		if(x!=p.x) return x>p.x;
                                        		if(y!=p.y) return y>p.y;
                                        		if(z!=p.z)return z>p.z;
                                        		return w>p.w;
                                        		//return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa4 &p) const{
                                        		return x==p.x && y==p.y && z==p.z &&w==p.w;
                                        	}
                                        		
                                        
                                        };
                                        class pa2{
                                        	public:
                                        	int x,y;
                                        	pa2(int x=0,int y=0):x(x),y(y) {}
                                        	pa2 operator + (pa2 p) {return pa2(x+p.x,y+p.y);}
                                        	pa2 operator - (pa2 p) {return pa2(x-p.x,y-p.y);}
                                        	bool operator < (const pa2 &p) const{
                                        		return y != p.y ? y<p.y: x<p.x;
                                        	}
                                        	bool operator > (const pa2 &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const pa2 &p) const{
                                        		return abs(x-p.x)==0 && abs(y-p.y)==0;
                                        	}
                                        	bool operator != (const pa2 &p) const{
                                        		return !(abs(x-p.x)==0 && abs(y-p.y)==0);
                                        	}
                                        		
                                        
                                        };
                                        
                                               #define ppa pair<int,pas>
                                        class Point{
                                        	public:
                                        	double x,y;
                                        	Point(double x=0,double y=0):x(x),y(y) {}
                                        	Point operator + (Point p) {return Point(x+p.x,y+p.y);}
                                        	Point operator - (Point p) {return Point(x-p.x,y-p.y);}
                                        	Point operator * (double a) {return Point(x*a,y*a);}
                                        	Point operator / (double a) {return Point(x/a,y/a);}
                                        	double absv() {return sqrt(norm());}
                                        	double norm() {return x*x+y*y;}
                                        	bool operator < (const Point &p) const{
                                        		return x != p.x ? x<p.x: y<p.y;
                                        	}
                                        	bool operator == (const Point &p) const{
                                        		return fabs(x-p.x)<EPS && fabs(y-p.y)<EPS;
                                        	}
                                        };
                                        typedef Point Vector;
                                 #define pl pair<int,pas>
                                        struct Segment{
                                        Point p1,p2;
                                        };
                                         double dot(Vector a,Vector b){
                                        	return a.x*b.x+a.y*b.y;
                                        }
                                        double cross(Vector a,Vector b){
                                        	return a.x*b.y-a.y*b.x;
                                        }
                                    
            bool parareru(Point a,Point b,Point c,Point d){
            //	if(abs(cross(a-b,d-c))<EPS)cout<<"dd "<<cross(a-b,d-c)<<endl;
            	return abs(cross(a-b,d-c))<EPS;
            }
            double distance_ls_p(Point a, Point b, Point c) {
              if ( dot(b-a, c-a) < EPS ) return (c-a).absv();
              if ( dot(a-b, c-b) < EPS ) return (c-b).absv();
              return abs(cross(b-a, c-a)) / (b-a).absv();
            }
            bool is_intersected_ls(Segment a,Segment b) {
            	if(a.p1==b.p1||a.p2==b.p1||a.p1==b.p2||a.p2==b.p2) return false;
            	if(parareru((a.p2),(a.p1),(a.p1),(b.p2))&&parareru((a.p2),(a.p1),(a.p1),(b.p1))){
            //		cout<<"sss"<<endl;
            		if(dot(a.p1-b.p1,a.p1-b.p2)<EPS) return true;
            		if(dot(a.p2-b.p1,a.p2-b.p2)<EPS) return true;
            		if(dot(a.p1-b.p1,a.p2-b.p1)<EPS) return true;
            		if(dot(a.p1-b.p2,a.p2-b.p2)<EPS) return true;
            		return false;
            	}
              else return ( cross(a.p2-a.p1, b.p1-a.p1) * cross(a.p2-a.p1, b.p2-a.p1) < EPS ) && ( cross(b.p2-b.p1, a.p1-b.p1) * cross(b.p2-b.p1, a.p2-b.p1) < EPS );
            }
             
            double segment_dis(Segment a,Segment b){
            	if(is_intersected_ls(a,b))return 0;
            	double r=distance_ls_p(a.p1, a.p2, b.p1);
            	r=min(r,distance_ls_p(a.p1, a.p2, b.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p2));
            	r=min(r,distance_ls_p(b.p1, b.p2, a.p1));
            	return r;
            }
            Point intersection_ls(Segment a, Segment b) {
              Point ba = b.p2-b.p1;
              double d1 = abs(cross(ba, a.p1-b.p1));
              double d2 = abs(cross(ba, a.p2-b.p1));
              double t = d1 / (d1 + d2);
             
              return a.p1 + (a.p2-a.p1) * t;
            }
             
                            string itos( int i ) {
                            ostringstream s ;
                            s << i ;
                            return s.str() ;
                            }
                             
                            int gcd(int v,int b){
                            	if(v>b) return gcd(b,v);
                            	if(v==b) return b;
                            	if(b%v==0) return v;
                            	return gcd(v,b%v);
                            }
             
                            double distans(double x1,double y1,double x2,double y2){
                            	double rr=(x1-x2)*(x1-x2)+(y1-y2)*(y1-y2);
                            	return sqrt(rr);
                            	
                            }
                            
   //         int pr[2000010];
     //       int inv[2000010];
            
            int beki(int wa,int rr,int warukazu){
            	if(rr==0) return 1%warukazu;
            	if(rr==1) return wa%warukazu;
            	if(rr%2==1) return (beki(wa,rr-1,warukazu)*wa)%warukazu;
            	int zx=beki(wa,rr/2,warukazu);
            	return (zx*zx)%warukazu;
            }
double bekid(double w,int r){
	if(r==0) return 1.0;
	if(r==1) return w;
	if(r%2) return bekid(w,r-1)*w;
	double f=bekid(w,r/2);
	return f*f;
}
            /*
			int comb(int nn,int rr){
				int r=pr[nn]*inv[rr];
				r%=inf;
				r*=inv[nn-rr];
				r%=inf;
				return r;
			}
            
            void gya(int ert){
            	pr[0]=1;
            	for(int i=1;i<ert;i++){
            		pr[i]=(pr[i-1]*i)%inf;
            	}
            	for(int i=0;i<ert;i++) inv[i]=beki(pr[i],inf-2,inf);
            	
            }
             */
			//priority_queue<pa3,vector<pa3>,greater<pa3>> pq;            
             //sort(ve.begin(),ve.end(),greater<int>());
                                     //----------------kokomade tenpure------------
            //vector<double> ans(100000000),ans2(100000000)



int hai[2][320*320];
int sabun[2][320]={0};
pa ansmax[2][320];
pa ansmin[2][320];
int D=320;

pa fmin(pa z1,pa z2){
	if(z1.first>z2.first) return z2;
	if(z1.first<z2.first) return z1;
	return mp(z1.first,z1.second+z2.second);
}


pa fmax(pa z1,pa z2){
	if(z1.first>z2.first) return z1;
	if(z1.first<z2.first) return z2;
	return mp(z1.first,z1.second+z2.second);
}

void tien(int df,int num){
	if(sabun[df][num]==0) return;
	
	for(int i=D*num;i<D*(num+1);i++)hai[df][i]+=sabun[df][num];
	
	ansmax[df][num].first+=sabun[df][num];
	ansmin[df][num].first+=sabun[df][num];
	sabun[df][num]=0;
}

void chousei(int df,int num){
	if(sabun[df][num]!=0) tien(df,num);
	pa z=mp(inf*100000ll,1);
	for(int i=D*num;i<D*(num+1);i++)z=fmin(z,mp(hai[df][i],1));
	ansmin[df][num]=z;
	z=mp(-inf*100000ll,1);
	for(int i=D*num;i<D*(num+1);i++)z=fmax(z,mp(hai[df][i],1));
	ansmax[df][num]=z;
	
}

void add(int df,int l,int r,int val){
int lb=l/D,rb=r/D;
	tien(df,lb);
	tien(df,rb);
	
	if(lb==rb){
		for(int i=l;i<=r;i++)hai[df][i]+=val;
		chousei(df,lb);
		return ;
	}
	
	for(int i=l;i<D*(lb+1);i++)hai[df][i]+=val;
	for(int i=D*rb;i<=r;i++)hai[df][i]+=val;
	chousei(df,lb);
	chousei(df,rb);
	for(int i=lb+1;i<rb;i++){
		sabun[df][i]+=val;
	}
}

pa rangemin(int df,int l,int r){
int lb=l/D,rb=r/D;
	tien(df,lb);
	tien(df,rb);
	pa z=mp(inf*100000ll,1);
	if(lb==rb){
		for(int i=l;i<=r;i++)z=fmin(z,mp(hai[df][i],1));
	return z;
	}
	for(int i=l;i<D*(lb+1);i++)z=fmin(z,mp(hai[df][i],1));
	for(int i=D*rb;i<=r;i++)z=fmin(mp(hai[df][i],1),z);	
	
	for(int i=lb+1;i<rb;i++){
	pa zz=ansmin[df][i];
		
	zz.first+=sabun[df][i];
		z=fmin(z,zz);
	}
	return z;
}


pa rangemax(int df,int l,int r){
int lb=l/D,rb=r/D;
	tien(df,lb);
	tien(df,rb);
	pa z=mp(-inf*100000ll,1);
	if(lb==rb){
		for(int i=l;i<=r;i++)z=fmax(z,mp(hai[df][i],1));
	return z;
	}
	for(int i=l;i<D*(lb+1);i++)z=fmax(z,mp(hai[df][i],1));
	for(int i=D*rb;i<=r;i++)z=fmax(mp(hai[df][i],1),z);	
	for(int i=lb+1;i<rb;i++){
	pa zz=ansmax[df][i];
	zz.first+=sabun[df][i];
		z=fmax(z,zz);
	}
	return z;
}

pa solve(pa z1,pa z2,pa z3,pa z4,int a,int b,int c,int d){
	if(z1.first==z2.first && z3.first==z4.first){
		return mp(z1.first*z3.first,z1.second*z3.second);
	}
	
	if(z1.first==z2.first){
		if(z1.first==0)return mp(0,(d-c+1)*z1.second);
		pa w1=mp(z1.first*z3.first,z1.second*z3.second);
		pa w2=mp(z1.first*z4.first,z1.second*z4.second);
		if(w1.first<w2.first)return w1;
		if(w1.first>w2.first)return w2;
		
	}
	if(z3.first==z4.first){
		if(z3.first==0)return mp(0,(b-a+1)*z3.second);
		pa w1=mp(z1.first*z3.first,z1.second*z3.second);
		pa w2=mp(z2.first*z3.first,z2.second*z3.second);
		if(w1.first<w2.first)return w1;
		if(w1.first>w2.first)return w2;
		
	}
	
	pa z=mp(z1.first*z3.first+1,1);
	pa w1=mp(z1.first*z3.first,z1.second*z3.second);
	pa w2=mp(z2.first*z3.first,z2.second*z3.second);
	pa w3=mp(z1.first*z4.first,z1.second*z4.second);
	pa w4=mp(z2.first*z4.first,z2.second*z4.second);
	
		z=fmin(z,w1);
		z=fmin(z,w2);
		z=fmin(z,w3);
		z=fmin(z,w4);
	
	if(z.first!=0)	return z;

	if(z1.first*z2.first==0 &&z3.first*z4.first==0 ){
		int d1,d2;
		if(z1.first==0)d1=z1.second;
		else d1=z2.second;
		if(z3.first==0)d2=z3.second;
		else d2=z4.second;
		
		return mp(0,(b-a+1)*(d-c+1)-(b-a+1-d1)*(d-c+1-d2));
	}
	
	if(z1.first*z2.first==0){
	int d1;
		if(z1.first==0)d1=z1.second;
		else d1=z2.second;
		return mp(0,d1*(d-c+1));
	}
	
	
	if(z3.first*z4.first==0){
	int d1;
		if(z3.first==0)d1=z3.second;
		else d1=z4.second;
		return mp(0,d1*(b-a+1));
	}
	exit(1);
}

void makemin(int df,int r){
	pa z=mp(inf*10000ll,1);
	for(int i=D*r;i<D*(r+1);i++)z=fmin(z,mp(hai[df][i],1));
	ansmin[df][r]=z;
}

void makemax(int df,int r){
	pa z=mp(-inf*10000ll,1);
	for(int i=D*r;i<D*(r+1);i++)z=fmax(z,mp(hai[df][i],1));
	ansmax[df][r]=z;
}

signed main(){
int h,w,q;
	cin>>h>>w>>q;
	for(int i=1;i<=h;i++)cin>>hai[0][i];
		for(int i=1;i<=w;i++)cin>>hai[1][i];
	
	for(int i=0;i<D;i++)makemin(0,i),makemin(1,i);
	for(int i=0;i<D;i++)makemax(0,i),makemax(1,i);
	for(int we=0;we<q;we++){
	int t;
		cin>>t;
		
		if(t==1){
			int a,b,c;
			cin>>a>>b>>c;
			add(0,a,b,c);
		}
		if(t==2){
		int a,b,c;
			cin>>a>>b>>c;
			add(1,a,b,c);
		}
		if(t==3){
		int a,b,c,d;
			cin>>a>>b>>c>>d;
			
			pa z1=rangemax(0,a,b);
			pa z2=rangemin(0,a,b);
			pa z3=rangemax(1,c,d);
			pa z4=rangemin(1,c,d);
		//	cout<<z2.first<<"  "<<z2.second<<endl;
			pa z=solve(z1,z2,z3,z4,a,b,c,d);
			cout<<z.first<<" "<<z.second<<endl;
		}
		
		if(t==4){
		int a,b,c,d;
			cin>>a>>b>>c>>d;
			
			pa z1=rangemax(0,a,b);
			pa z2=rangemin(0,a,b);
			pa z3=rangemax(1,c,d);
			pa z4=rangemin(1,c,d);
			z1.first*=-1;
			z2.first*=-1;
			pa z=solve(z1,z2,z3,z4,a,b,c,d);
			cout<<-z.first<<" "<<z.second<<endl;
		}
	
	}
	
 return 0;
        }